Arithmetic Progressions
Arithmetic Progression (AP) also known as Arithmetic Sequence is a sequence or series of numbers such that the common difference between two consecutive numbers in the series is constant.
For example:
- Series 1: 1,3,5,7,9,11….
In this series, the common difference between any two consecutive numbers is always 2.
- Series 2: 28,25,22,19,16,13….
In this series, the common difference between any two consecutive numbers is strictly -3.
Terminology and Representation in Arithmetic Progressions
- Common difference, d = a2 – a1 = a3 – a2 = ……. = an – an – 1
- an = nth term of Arithmetic Progression
- Sn = Sum of first n elements in the series
Arithmetic Progressions Class 10: NCERT Notes
Arithmetic progression(AP) also called an arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence
A progression is a sequence or series of numbers in which they are arranged in a particular order such that the relation between the consecutive terms of a series or sequence is always constant. In a progression, it is possible to obtain the nth term of the series.
In mathematics, there are 3 types of progressions:
- Arithmetic Progression (AP)
- Geometric Progression (GP)
- Harmonic Progression (HP)
let’s learn about AP in this article.
Table of Content
- Arithmetic Progressions
- Nth Term of an AP
- General Form of an AP
- Sum of n Terms of Arithmetic Progression
- Sample Problems on Arithmetic Progressions
- Practice Questions on Arithmetic Progression
- Arithmetic Progression-FAQs